For the function f(x,y)=x2−2xy+4y3 find all stationary point. As an answer, please, provide the product of its coordinates' means. If there is no stationary points. write −1000.
Yes, you have found the local minimum at (1/6;1/6) and non extremum at (0;0)!
Find the number of extrema of the function f(x,y)=(x−1)2+y2−4y. If there is no extrema, write −1.
Correct!
Choose correct statements (there could be more than one answer). In case of only positive arguments x,y>0, the function f(x,y)=Cxα+1yβ+1, C,α,β≥0, α+β<1:
Correct!
Correct!
Assume the function f(x,y)=x/y2 is given with a condition (restriction) y−x+1=0. Amongst all the points that statisfy the condition, find extremal ones and write the x coordinate of the minimum.
Correct!
Consider the function (x2+y2)e−x2−y2. Provide the number of maxima of f(x,y). In case there is no maxima, write −1; in case there is infinite number of maxima, write −2.
Correct!